Convex geometry inequality and equality-case workbench

Family 087: The Mahler conjectures, functional inequalities and polar-product symplectic width. First review, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Geometry researchers can compare volume products, polar bodies and equality families; symplectic researchers can review the polar-product width statement.

Applicability and commercial boundary

These are exact geometric inequalities, not a finite mesh algorithm or a production packing optimizer. Computing volumes and verifying convexity introduce separate costs.

Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses.

Next verification action

Inspect equality constructions and identify a finite exact reference case.

Evidence scope

The catalog statement was individually reviewed. Main-paper and selected formal-scope passages were additionally inspected for families 090, 093, 094, 097, 325, 328 and 332; this record does not claim a full proof audit or independent Lean verification. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.